A226728 G.f.: 1/G(0), where G(k) = 1 + q^(k+1) / (1 - q^(k+1)/G(k+2) ).

1, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, -4, 0, 0, 0, 4, 0, 0, 0, -3, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 0, -6, 0, 0, 0, 7, 0, 0, 0, -5, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, -9, 0

Offset: 0

Author

Joerg Arndt, Jun 29 2013

Keywords

• sign

Crossrefs

Cf. A049346 (g.f.: 1 - 1/G(0), G(k)= 1 + q^(k+1) / (1 - q^(k+1)/G(k+1) ) ).

Cf. A226729 (g.f.: 1/G(0), G(k) = 1 - q^(k+1) / (1 - q^(k+1)/G(k+2) ) ).

Cf. A006958 (g.f.: 1/G(0), G(k) = 1 - q^(k+1) / (1 - q^(k+1)/G(k+1) ) ).

Cf. A227309 (g.f.: 1/G(0), G(k) = 1 - q^(k+1) / (1 - q^(k+2)/G(k+1) ) ).

Programs

PARI

N = 166;  q = 'q + O('q^N);
G(k) = if(k>N, 1, 1 + q^(k+1) / (1 - q^(k+1) / G(k+2) ) );
gf = 1 / G(0);
Vec(gf)

Formula

G.f.: 1/(1+q/(1-q/(1+q^3/(1-q^3/(1+q^5/(1-q^5/(1+q^7/(1-q^7/(1+ ... ))))))))).

G.f.: 1/W(0), where W(k)= 1 + x^(2*k+1)/(1 - x^(2*k+1)/W(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Aug 16 2013